标题： 规范系统的特征值分布：迹类和稀疏谱 显示英文标题

标题： Eigenvalue distribution of canonical systems: trace class and sparse spectrum

摘要： 在本文中，我们考虑具有离散谱的二维规范系统，并研究它们的特征值密度。 我们推导了一个公式，该公式可以确定特征值计数函数的Stieltjes变换，仅相差普遍的乘法常数。 给出了模型算子的预解式属于索引为0<p<2的Schatten-von Neumann类的显式准则，从而回答了一个长期存在的问题，即哪些规范系统具有迹类预解式。 对于具有两个极限圆端点的规范系统，我们开发了一个算法，用于确定单色矩阵的增长，误差很小。 此外，我们提供了示例来说明我们的结果，展示了它们的精确性，并证明了一个逆结果，给出了显式公式。 显示英文摘要

摘要： In this paper we consider two-dimensional canonical systems with discrete spectrum and study their eigenvalue densities. We develop a formula that determines the Stieltjes transform of the eigenvalue counting function up to universal multiplicative constants. An explicit criterion is given for the resolvents of the model operator to belong to a Schatten-von Neumann class with index 0<p<2, thus giving an answer to the long-standing question which canonical systems have trace class resolvents. For canonical systems with two limit circle endpoints we develop an algorithm for determining the growth of the monodromy matrix up to a small error. Moreover, we present examples to illustrate our results, show their sharpness and prove an inverse result giving explicit formulae.